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The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of time fractional model analysis in which initial conditions are involved.

The flow resulting from the rotation of a series of thin plates that initially separate two gases of different densities is analyzed using direct numerical simulations (DNSs). The 90-deg plates' rotation forms a vorticity shear layer and a density interface in between the tips of two neighboring plates. Results of this study show that the shape of these layers strongly depends on the plate's tip-based Reynolds number that can be varied thanks to a parametrization of the plates' opening law. Different regimes are identified corresponding to single- or multimode initial interfaces, with or without the occurrence of starting vortices during the formation of the shear layer. The density interfaces resulting from this procedure are particularly well-suited to serve as initial conditions for the study of the Richtmyer–Meshkov (RM) instability-induced mixing. Results of this study also provide a description of vortex formation in stratified flows.

We present Atacama Large Millimeter/sub-millimeter Array (ALMA) observations towards 27 low-redshift ($0.02< z, 16 pages, 10 figures to be published in MNRAS

The ricochet behaviour of the air–water trans-media vehicle (AWTMV) during water-entry crossing was experimentally investigated. Three types of small-scale AWTMV including cone, ogive, and flat nose were used in the test. The underwater trajectory, velocity, and inclination angle of projectiles during the ricochet process were obtained using a high-speed camera. The angle change of the AWTMV and the ratio of the residual velocity are introduced. Based on this result, the relationship between the ricochet responses and initial conditions was derived. The results of this study show that (1) a small incident angle and great velocity make the occurrence of ricochet behaviour easier, (2) the stability of the trajectory of projectiles with cone, ogive, and flat nose weakened in turn at the same initial conditions, (3) the angle change and the ratio of the residual velocity are linear functions of the incident angle and velocity.

Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.

Assuming that the equilibrium geometry of river channels does not depend on their initial state but solely on boundary conditions, several formulas have been derived that relate the channel depth and width to the river bankfull discharge and bed material. However, due to the existence of a threshold for sediment motion and the strong non-linearity between sediment transport and flow rate, this assumption might not be generally valid for gravel-bed rivers. This research clarifies the role of the initial conditions, more specifically the initial channel width, on the geometry of gravel-bed rivers considering a variety of boundary conditions. The approach includes laboratory experiments and two-dimensional modeling, reproducing the evolution of alluvial channels with different starting widths, discharge regimes and sediment input rates. The experiments represent the Arc River (France). Thus, the characteristics of this river were used in the numerical model to obtain a realistic virtual case complementing the experiments. Different boundary and starting conditions resulted in either braided or single-thread channels. We found that the initial width strongly influences the evolution process and leaves a footprint on the river braid-belt extension. The active width of braided systems and the width of single-thread channels do not depend on the starting condition. They depend on sediment input rather than on discharge variability. Different initial widths result in different final bed levels. This indicates that the initial channel width may affect the degree of channel incision or aggradation. The results of this study justify the use of equilibrium formulas for single-thread rivers.

Indeterminate equilibrium rational expectations (RE) models are ubiquitous in both theoretical and applied work in dynamic macroeconomics. The issue of characterizing the exact dimension of indeterminacy—i.e. of deriving the full set of causal and stable solutions to linear RE models—has only recently been addressed in the context of general and multivariate settings. This paper complements existing results by identifying bounds on the observable dimension of indeterminacy of linear RE models in the presence of arbitrary initial conditions. Implications for the estimation of indeterminate equilibrium RE models are discussed.

In this article, we focus on a class of singular linear systems of fractional differential equations with given nonconsistent initial conditions (IC). Because the nonconsistency of the IC can not lead to a unique solution for the singular system, we use two optimization techniques to provide an optimal solution for the system. We use two optimization techniques to provide the optimal solution for the system because a unique solution for the singular system cannot be obtained due to the non-consistency of the IC. These two optimization techniques involve perturbations to the non-consistent IC, specifically, an l2 perturbation (which seeks an optimal solution for the system in terms of least squares), and a second-order optimization technique at an l1 minimum perturbation, (which includes an appropriate smoothing). Numerical examples are given to justify our theory. We use the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo-Fabrizio (CF) and the Atangana-Baleanu (AB) fractional derivative. Science Foundation Ireland

Purpose: Gross Domestic Product(GDP) depends on Agriculture, Service, and industry performance. The main aim of the study is to assess the relationship between dependent variable GDP and Independent variables agriculture, industry, and service sector by using the n-variable Regression Model at initial condition. Design/Methodology/Approach: The study is an application of the n-variable Regression Model at the initial condition to analyze the situation of GDP along with reasons not becoming zero GDP even after using the initial condition. The secondary data of the GDP of Nepal from the Central Bureau of Statistics of 10 years till 2019/20 has been analyzed. By finding cofactors of correlation coefficient matrix, Mean and standard deviation of the individual data to establish the linear relationship between dependent and independent variable. Findings/Result: Under initial conditions, if all the independent variables zero, the GDP is −751028.431 billion, negative sign shows that GDP decreases highly if the entire major factor has no role in GDP. It is non-zero GDP. It means in the 11th year the stated amount will be expended from the previous year saving for forex to import which will not be possible in a sustainable economy. It will not be possible in real conditions however it may be hypothetical possible either because of the impact of informal economy or disinvestment or negative net exports. It is significant for forecasting the future GDP of a country effectively assuming different conditions for policy formulation. Originality/Value: It is the first empirical research using the n-variable Regression Model for GDP Analysis. Paper Type: Analytical Policy Research

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The origins of uncertainty in climate projections have major consequences for the scientific and policy decisions made in response to climate change. Internal climate variability, for example, is an inherent uncertainty in the climate system that is undersampled by the multimodel ensembles used in most climate impacts research. Because of this, decision makers are left with the question of whether the range of climate projections across models is due to structural model choices, thus requiring more scientific investment to constrain, or instead is a set of equally plausible outcomes consistent with the same warming world. Similarly, many questions faced by scientists require a clear separation of model uncertainty and that arising from internal variability. With this as motivation and the renewed attention to large ensembles given planning for Phase 7 of the Coupled Model Intercomparison Project (CMIP7), we illustrate the scientific and policy value of the attribution and quantification of uncertainty from initial condition large ensembles, particularly when analyzed in conjunction with multimodel ensembles. We focus on how large ensembles can support regional‐scale robust adaptation decision‐making in ways multimodel ensembles alone cannot. We also acknowledge several recently identified problems associated with large ensembles, namely, that they are (1) resource intensive, (2) redundant, and (3) biased. Despite these challenges, we show, using examples from hydroclimate, how large ensembles provide unique information for the scientific and policy communities and can be analyzed appropriately for regional‐scale climate impacts research to help inform risk management in a warming world., Earth's Future, 8 (10), ISSN:2328-4277

We present the results of a single-pointing survey of 207 dense cores embedded in Planck Galactic Cold Clumps distributed in five different environments ($\lambda$ Orionis, Orion A, B, Galactic plane, and high latitudes) to identify dense cores on the verge of star formation for the study of the initial conditions of star formation. We observed these cores in eight molecular lines at 76-94 GHz using the Nobeyama 45-m telescope. We find that early-type molecules (e.g., CCS) have low detection rates and that late-type molecules (e.g., N$_2$H$^+$, c-C$_3$H$_2$) and deuterated molecules (e.g., N$_2$D$^+$, DNC) have high detection rates, suggesting that most of the cores are chemically evolved. The deuterium fraction (D/H) is found to decrease with increasing distance, indicating that it suffers from differential beam dilution between the D/H pair of lines for distant cores ($>$1 kpc). For $\lambda$ Orionis, Orion A, and B located at similar distances, D/H is not significantly different, suggesting that there is no systematic difference in the observed chemical properties among these three regions. We identify at least eight high D/H cores in the Orion region and two at high latitudes, which are most likely to be close to the onset of star formation. There is no clear evidence of the evolutionary change in turbulence during the starless phase, suggesting that the dissipation of turbulence is not a major mechanism for the beginning of star formation as judged from observations with a beam size of 0.04 pc., Comment: 55 pages, 12 Figures, 8 Tables, accepted for publication in ApJS

Free-falling paper shapes exhibit rich, complex and varied behaviours that are extremely challenging to model analytically. Physical experimentation aids in system understanding, but is time-consuming, sensitive to initial conditions and reliant on subjective visual behavioural classification. In this study, robotics, computer vision and machine learning are used to autonomously fabricate, drop, analyse and classify the behaviours of hundreds of shapes. The system is validated by reproducing results for falling discs, which exhibit four falling styles: tumbling, chaotic, steady and periodic. A previously determined mapping from a non-dimensional parameter space to behaviour groups is shown to be consistent with these new experiments for tumbling and chaotic behaviours. However, steady or periodic behaviours are observed in previously unseen areas of the parameter space. More complex hexagon, square and cross shapes are investigated, showing that the non-dimensional parameter space generalizes to these shapes. The system highlights the potential of robotics for the investigation of complex physical systems, of which falling paper is one example, and provides a template for future investigation of such systems. The dynamics of paper shapes in free fall are still not fully understood, despite being discussed for more than 150 years. Collecting large amounts of data has the potential to give us new insights and a robotics system could generate and analyse data in large quantities.

In the last thirty years, agent-based modelling has become a well-known technique for studying and simulating dynamical systems. Still, there are some open issues to be addressed. One of these is the substantial absence of studies about the sensitivity to initial conditions, that is the effect of small variations at the beginning of simulation on the macro-level behaviour of the model. The goal of this preliminary work is to explore how a single modification on one agent affects the evolution of the simulation. Through the analysis of two deterministic models (a simple market model and Reynolds’ flocking model), we obtain two main results. First, we observe that the impact of the variation of a single initial condition on the simulation behaviour is high in both models. Second, there is evidence of an at least qualitative relation between some general agent-based model settings (numerosity of agents in the model and rate of connections between agents) and the sensitivity to the modified initial condition. We conclude that at least some significant classes of agent-based models are affected by a high sensitivity to initial conditions that have a negative effect on the predictive power of simulations.

The action of loop quantum gravity includes the Holst term and/or the Nieh-Yan term in addition to the Ricci scalar. These terms are expected to couple non-minimally to the Higgs. Thus the Holst and Nieh-Yan terms contribute to the classical equations of motion, and they can have a significant impact on inflation. We derive inflationary predictions in the parameter space of the non-minimal couplings, including non-minimally coupled terms up to dimension 4. Successful inflation is possible even with zero or negative coupling of the Ricci scalar. Notably, inflation supported by the non-minimally coupled Holst term alone gives almost the same observables as the original metric formulation plateau Higgs inflation. A non-minimally coupled Nieh-Yan term alone cannot give successful inflation. When all three terms are considered, the predictions for the spectral index and tensor-to-scalar ratio span almost the whole range probed by upcoming experiments. This is not true for the running of the spectral index, and many cases are highly tuned., Comment: 16+9 pages, 1 figure. Corrected typos and one figure, added references and explanations. Published version

In this paper, dynamic elasticity equations for one-dimensional (1D) quasicrystals (QCs) with arbitrary system of anisotropy are considered. Fundamental solutions (FSs) of the phonon–phason displacements, displacement speeds, and stresses arising from pulse point sources are computed. New existence, uniqueness and stability estimate theorems are obtained for dynamic elasticity equations in 1D QCs with the initial conditions (ICs). As a computational example, FS components are computed for orthorhombic and triclinic structures in 1D QCs. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

A method is presented to obtain initial conditions for Smoothed Particle Hydrodynamic (SPH) scenarios where arbitrarily complex density distributions and low particle noise are needed. Our method, named ALARIC, tampers with the evolution of the internal variables to obtain a fast and efficient profile evolution towards the desired goal. The result has very low levels of particle noise and constitutes a perfect candidate to study the equilibrium and stability properties of SPHISPMHD systems. The method uses the iso-thermal SPH equations to calculate hydrodynamical forces under the presence of an external fictitious potential and evolves them in time with a 2nd-order symplectic integrator. The proposed method generates tailored initial conditions that perforrri better in many cases than those based on purely crystalline lattices, since it prevents the appearance of anisotropies. The authors would like to thank J.M. Reynolds, D. Price and F. Stasyszyn for the fruitful conversations which, although brief in duration, were rich in content and helped shape the contents of this paper. This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265 and the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC. The authors thank the editor and referees for the constructive comments and their patience.

Modelling of the pavement temperature facilitates winter road maintenance. It is used for predicting the glaze formation and for scheduling the spraying of the de-icing brine. The road weather is commonly forecasted by solving the energy balance equations. It requires setting the initial vertical profile of the pavement temperature, which is often obtained from the Road Weather Information Stations. The paper proposes the use of average air temperature from seven preceding days as a pseudo-observation of the subsurface temperature. Next, the road weather model is run with a few days offset. It first uses the recent, historical weather data and then the available forecasts. This approach exploits the fact that the energy balance models tend to “forget” their initial conditions and converge to the baseline solution. The experimental verification was conducted using the Model of the Environment and Temperature of Roads and the data from a road weather station in Warsaw over a period of two years. The additional forecast error introduced by the proposed pseudo-observational initialization averages 1.2 °C in the first prediction hour and then decreases in time. The paper also discusses the use of Digital Surface Models to take into account the shading effects, which are an essential source of forecast errors in urban areas. Limiting the use of in-situ sensors opens a perspective for an economical, largescale implementation of road meteorological models.

A mathematical model has been proposed for the development of single twin layers in metal crystals under various loading regimes and various conditions. The model parameters depend on the geometric characteristics of the twin layer, the physical characteristics of the crystal, the Burgers vector, and the motion velocity of twin dislocations. Methods for the determination of the phenomenological parameters from experimental data were developed. In some cases, a comparison of the parameter values calculated in the framework of the proposed mathematical model with those obtained from experimental data was made, which demonstrated their satisfactory consistency. The proposed model can be useful for the development of a quantitative theory of twinning., Запропоновано математичну модель розвитку одиничних двiйникових прошаркiв у металевих кристалах при рiзних режимах навантаження, за рiзних умов. Параметри моделi залежать вiд геометричних характеристик двiйникового прошарку, фiзичних характеристик кристала, вектора Бюргерса та швидкостi руху двiйникових дислокацiй. Розроблено методики вiдновлення феноменологiчних параметрiв з експериментальних даних. У низцi випадкiв проведено порiвняння значень параметрiв, що обчислено згiдно з запропонованою математичною моделлю, з тими, якi отримано з даних експерименту. Порiвняння показує задовiльну узгодженiсть. Запропонована модель може бути корисною в створеннi кiлькiсної теорiї двiйникування.

Using a small number of mathematical transformations, this article examines the nature of fractional models described by fractional differential equations or pseudo state space descriptions. Computation of the impulse response of a fractional model using the Cauchy method shows that they exhibit infinitely small and high time constants. This impulse response can be rewritten as a diffusive representation whose Fourier transform permits a representation of a fractional model by a diffusion equation in an infinite space domain. Fractional models can thus be viewed as doubly infinite dimensional models: infinite as distributed with a distribution in an infinite domain. This infinite domain or the infinitely large time constants of the impulse response reveal a property intrinsic to fractional models: their infinite memory. Solutions to generate fractional behaviors without infinite memory are finally proposed.

Opinion polls may inadvertently affect public opinion, as people may change their attitudes after learning what others think. A disconcerting possibility is that opinion polls have the ability to create information cascades, wherein the majority opinion becomes increasingly larger over time. Testing poll influence on attitudes toward Syrian refugees and mandatory measles vaccination, we field survey experiments on a probability-based online survey panel. Through a novel automated procedure labeled the dynamic response feedback, we measure whether the answers from early poll respondents can influence the opinions of subsequent respondents who learn the answers of the previous respondents. Using this procedure, no feedback loops are identified.

With increasing dependence on communications over internet and networks, secure data transmission is coming under threat. One of the best solutions to ensure secure data transmissions is encryption. Multiple forms of data, such as text, audio, image, and video can be digitally transmitted, nowadays images being the most popular and old encryption techniques such as: AES,DES,RSA etc., show low security level when used for image encryption. This problem was resolved by using of chaos encryption which is an acceptable form of encryption for image data. The sensitivity to initial conditions and control parameters make chaos encryption suitable for image applications. This study discusses various chaos encryption techniques.

Agricultural biomass burning (ABB) has been of particular concern due to its influence on air quality and atmospheric radiation, as it produces large amounts of gaseous and aerosol emissions. This paper presents an integrated observation of a significant ABB episode in Nanjing, China, during early June 2011, using combined ground-based and satellite sensors (Moderate Resolution Imaging Spectroradiometer, Atmospheric Infrared Sounder, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), and Ozone Monitoring Instrument products). The time-height distribution, optical properties, sources and transport of smoke, and its impacts on air quality are investigated. Lidar profiles indicate that the smoke aerosols are confined to the planetary boundary layer (PBL) and have a depolarization ratio of less than 0.08. The aerosol optical depths increase from 0.5 to 3.0 at 500 nm, while the extinction-related Angstrom exponent increases from 1.1 to 1.6 at the wavelength pair of 440–870 nm. The single-scattering albedo becomes lower at 670–1020 nm following the ABB intrusion and particularly shows a decreasing tendency between wavelengths of 440 to 1020 nm. The absorption Angstrom exponent (0.7) is smaller than 1.0, which may indicate the aged smoke particles mixed or coated with the urban aerosols. Surface particular matter PM10 and PM2.5 show a dramatic increase, reaching hourly mean of 800 µg/m3 and 485 µg/m3, respectively, which results in a heavy air pollution event. The stagnant and high-moisture weather provides favorable conditions for the aerosols to accumulate near the surface. Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) also illustrate that the large-scale aerosols are primarily present in the PBL and transported to the ocean, but some dense smoke plumes are misclassified as cloud or polluted dust. By comparing with the observations, we found that the Weather Research and Forecasting–Chemistry model captured the accumulation and downwind transport of surface PM2.5 from 20:00 on 2 June to 10:00 on 3 June (phase 1) but showed a dramatic underestimate from 20:00 on 3–4 June (phase 2) when dense aerosols are present. Such a discrepancy in the model is associated with the improper vertical apportion of transported smoke and atmospheric diffusion conditions when comparing with the observed aerosol and wind profiles. In addition, the model simulations indicate that the transported smoke can contribute to 50–70% of the ground-level PM2.5 in Nanjing.

Ecosystem models require the specification of initial conditions, and these initial conditions have some level of uncertainty. It is important to allow for uncertainty when presenting model results, because it reduces the risk of errant or non-representative results. It is crucial that model results are presented as an envelope of what is likely, rather than presenting only one instance. We perturbed the initial conditions of the Chatham Rise Atlantis model and analysed the effect of this uncertainty on the model’s dynamics by comparing the model outputs resulting from many initial condition perturbations. At the species group level, we found some species groups were more sensitive than others, with lower trophic level species groups generally more sensitive to perturbations of the initial conditions. We recommend testing for robust system dynamics by assessing the consistency of ecosystem indicators in response to fishing pressure under perturbed initial conditions. In any set of scenarios explored using complex end-to-end ecosystem models, we recommend that associated uncertainty analysis be included with perturbations of the initial conditions.

In this research, uncertainty associated with initial and boundary conditions is evaluated for short-term wind speed prediction in complex terrain. The study area is the Alaiz mountain range, a windy region in the northern Iberian Peninsula. A multiphysics and multiple initial and boundary condition ensemble prediction system (EPS) was generated using the Weather Research and Forecasting model. Uncertainty of the EPS is analyzed using an index based on the spread between ensemble members, considering its behavior under different wind speed and direction events, and also during distinct atmospheric stability conditions. The results corroborate that physical parameterization uncertainty is greater for short-term forecasts (63.5%). However, it is also necessary to consider the uncertainty associated with initial conditions, not only for its quantitative importance (36.5%) but also for its behavior during thermal inversion conditions in the narrow valleys surrounded by mountains. This work was partially supported by research projects METEORISK (RTC-2014-1872-5), PCIN-2014-013-C07-04 and PCIN2016-080 (UE ERA-NET Plus NEWA Project), ESP2013 47816-C4-4-P, CGL2010-15930, CGL2016-78702-C2-1-R and CGL2016-78702-C2-2-R, CGL2016-81828-REDT, and the Instituto de Matemática Interdisciplinar (IMI) of the Universidad Complutense.

After reviewing commutativity of second-order linear time-varying analog systems, the inverse commutativity conditions are derived for these systems by considering non-zero initial conditions. On the base of these conditions, the transitivity property is studied for second order linear time-varying unrelaxed analog systems. It is proven that this property is always valid for such systems when their initial states are zero; when non-zero initial states are present, it is shown that the validity of transitivity does not require any more conditions and it is still valid. Throughout the study it is assumed that the subsystems considered can not be obtained from each other by any feed-forward and feed-back structure. The results are well validated by MATLAB simulations., Comment: 26 pages, 4 figures

In this paper, we conduct a mathematical analysis of the model of ensuring the road trains movement stability by changing the design of coupling devices to determine the critical characteristic parameters of the road trains, which result in the loss of en-route directional stability under external action. The concept of the model was to separate the process of yawing of the road trains and its elements (due to external perturbing action) on the highway into several typical stages. The main parameters of the stages (the displacement amplitude and rotation angle of the road trains elements in relation to the driving direction) were determined based on the initial conditions of the road trains movement, the force and duration of the external action. The most dangerous areas of external action application to the road trains were determined in this paper. The maximum permissible exposure limit should not exceed 0.5–1.0% of the road trains trailer momentum, with duration having the greater effect than the amount of impact. The results obtained can be used in mechanical engineering to improve the road trains performance.

One-of-a-kind experimental and numerical investigation is provided in this paper about energy sheet pile walls: earth retaining structures that embed heat exchanger probes within piles for the exploitation of shallow geothermal energy. The study resorts to the results of full-scale in situ tests and coupled three-dimensional thermo-mechanical finite element analyses of an energy sheet pile wall constructed in an underground station. In this context, an investigation about the influence of thermal boundary and initial conditions on thermo-mechanical behaviour of the energy sheet pile wall is performed. The addressed thermal boundary conditions are associated with the thermal load imposed on the considered foundation by the field environment and the geothermal operation of some energy piles constituting the wall. The addressed thermal initial conditions are associated with the undisturbed ground temperature field of the considered site. Based on a comparison between the experimental and numerical results, and the development of numerical sensitivity analyses, criticalities associated with the analysis and modelling of the thermo-mechanical behaviour of energy sheet pile walls are denoted. The results highlight that: a marked non-uniformity of the temperature field can characterise real applications of energy sheet pile walls, representing a significant challenge to capture numerically at all spatial locations; a comparable influence denotes thermal loads that derive from the field environment and the geothermal operation of energy sheet pile walls, deserving attention when modelling the behaviour of such geostructures; and a critical role of the initial thermal conditions is connected to the satisfactory understanding and prediction of the thermo-mechanical behaviour of energy sheet pile walls, requiring careful consideration for analysis and design purposes.

Numerous evacuation models are now able to represent populations with different movement abilities. However, this representation is not always supported by empirical data; i.e. the functionality can occasionally overreach the empirical support for it. The goals of this work are: (1) to provide data that adds to the understanding and quantification of vulnerable population's evacuation performance, and (2) to provide sufficiently detailed and transparent data-sets for model configuration and validation. Data was collected during five evacuations from the same school, conducted between 2011 and 2014. Children from 4 to 16 years old were involved in these drills. Four of the evacuations were unannounced, while one was semi-announced (i.e. staff were aware that the drill would be conducted on a particular day). In addition to the initial scenario conditions (e.g. the building geometry, population, procedures employed, etc.), a number of different performance data-sets were collected: pre-evacuation times, travel speeds, route use and evacuation arrival curves. Through the provision of detailed architectural diagrams and other initial conditions and raw data/analysis describing evacuee performance it is hoped that this data-set will be used in the development of evacuation models and their application. The limitations in the data collection and analysis process are outlined allowing the modeler to identify where issues might arise and take corrective actions where possible. Language: en

In this paper, we study turbulent mixing between two miscible fluids that is induced gravitationally by Rayleigh–Taylor instability in a tightly confined domain. In our experimental configurations, one lateral dimension is between two and three orders of magnitude smaller than the other. Our motivation is to examine the relationship between domain width and certain key flow statistics, as the geometric restriction changes in relative significance. We match our experiments with carefully-resolved numerical simulations and in order to impose appropriate initial conditions, we extend Taylor’s linear model of instability growth to characterise the influence of geometry on early modal development and use measured experimental data to inform our initialisation. We find that our experiments exhibit initial conditions with a k − 1 spectral scaling of interfacial perturbation of volume fraction with a high degree of repeatability, where k denotes wavenumber. We discovered that our form of geometric restriction couples favourably with the spectral composition of our initial condition. We observe no early-stage transient relaxation towards self–similarity, because the instability already begins in that stable self-similar equilibrium, and this important special case has not previously been noticed despite decades of related research. We present our statistical observations from both experiment and numerical simulation as a validation resource for the community; such simulations are inexpensive to compute yet capture many dynamically significant properties.

Summarization: A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given. Presented on

Context. Pre-stellar cores (PSCs) are units of star formation. Besides representing early stages of the dynamical evolution leading to the formation of stars and planets, PSCs also provide a substrate for incipient chemical complexity in the interstellar space. Aims. Our aim is to understand the influence of external conditions on the chemical composition of PSCs. For this purpose, we compared molecular column densities in two typical PSCs, L183 and L1544, which are embedded in different environments. Methods. A single-pointing survey of L183 at λ = 3 mm was conducted using the IRAM 30-m single-dish antenna. This led to the detection of more than 100 emission lines from 46 molecular species. The molecular column densities and excitation temperatures derived from these lines were compared to the corresponding parameters in L1544. The data for L1544 were obtained from literature or publicly available surveys, and they were analysed using the same procedure as adopted for L183. An astrochemical model, previously developed for the interpretation of organic molecule emissions towards the methanol peak of L1544, was used to interpret the combined data. Results. Our analysis reveals clear chemical differences between the two PSCs. While L1544 is richer in carbon-bearing species, in particular carbon chains, oxygen-containing species are generally more abundant in L183. The results are well-reproduced by our chemical model. Conclusions. The observed chemical differentiation between the two PSCs is caused by the different environmental conditions: the core of L183 is deeply buried in the surrounding cloud, whereas L1544 lies close to the edge of the Taurus Molecular Cloud. The obscuration of L183 from the interstellar radiation field (ISRF) allows the carbon atoms to be locked in carbon monoxide, which ultimately leads to a large abundance of O-bearing species. In contrast, L1544, being more affected by the ISRF, can keep a fraction of carbon in atomic form, which is needed for the production of carbon chains. © V. Lattanzi et al. 2020. Latvijas ZinÄ tnes Padome: lzp-2018/1-0170 for fruitful comments on the SO2 chemistry. Evelyne Roueff is also gratefully acknowledged for discussions on reaction rates of some complex organic molecules in our model. We also thank Elena Redaelli for providing the L1544 SPIRE density profile. The work by A.I.V. is supported by Latvian Council of Science via the Project lzp-2018/1-0170.

Agradecimentos: O. F. was supported by SFB-Transregio 33 'The Dark Universe' by the Deutsche Forschungsgemeinschaft (DFG). Support for D. G. was provided by NASA through Einstein Postdoctoral Fellowship Grant No. PF5-160138 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract No. NAS8-03060. O. F. and S. H. acknowledge support by the DFG cluster of excellence 'Origin and Structure of the Universe' (www.universe-cluster.de). Part of our computations have been carried out on the computing facilities of the Computational Center for Particle and Astrophysics (C2PAP). This paper has gone through internal review by the DES collaboration. We want to thank all the members of the DES WL, LSS and Theory working groups that have contributed with helpful comments and discussions. We also want to thank the anonymous journal referee for very helpful comments. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The DES data management system is supported by the National Science Foundation under Grant No. AST-1138766. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciencies de l'Espai (IEEC/CSIC), the Institut de Fisica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University. The DES participants from Spanish institutions are partially supported by MINECO under Grants No. AYA2012-39559, No. ESP2013-48274, No. FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234. Research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) including ERC Grant Agreements No. 240672, No. 291329, and No. 306478. D. G. is an Einstein Fellow Abstract: We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our earlier work on trough lensing and is summarized as follows: given a foreground (low redshift) population of galaxies, we divide the sky into subareas of equal size but distinct galaxy density. We then measure lensing around uniformly spaced points separately in each of these subareas, as well as counts-in-cells statistics (CiC). The lensing signals trace the matter density contrast around regions of fixed galaxy density. Through the CiC measurements this can be related to the density profile around regions of fixed matter density. Together, these measurements constitute a powerful probe of cosmology, the skewness of the density field and the connection of galaxies and matter. In this paper we show how to model both the density split lensing signal and CiC from basic ingredients: a non-linear power spectrum, clustering hierarchy coefficients from perturbation theory and a parametric model for galaxy bias and shot-noise. Using N-body simulations, we demonstrate that this model is sufficiently accurate for a cosmological analysis on year 1 data from the Dark Energy Survey FINANCIADORA DE ESTUDOS E PROJETOS - FINEP FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIRO - FAPERJ CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ MINISTÉRIO DA CIÊNCIA, TECNOLOGIA, INOVAÇÕES E COMUNICAÇÕES - MCTI Aberto

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian Baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decrease after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale $R_s$ larger than around 10$h^{-1}$Mpc. On smaller $R_s$,however, the deviation from the linear spectrum becomes significant on large scales ($k\lt R_s^{-1}$) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small $k$ after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime., Comment: 18 pages, 7 figures, accepted for publications in PRD

The article proposes a methodology for the analysis of the logical structure of the time and plot in Jorge Luis Borges’ short story “The Garden of Forking Paths” (1941). It builds on the ways Borges transmutes mathematical aesthetics into language through the lens of chaos theory and its links with literature. It becomes apparent that “The Garden” is a metaphor for a mathematical concept of time and its infinite bifurcations. This analysis of the ‘orderly disordered’ narrative focuses on the three main properties of chaotic systems in “The Garden”. Secondly, temporal iteration and folding become the main structural devices employed by establishing analogies among fictional levels. In “The Garden”, Borges describes a novel by Ts’ui Pên whose plot bifurcates at every point in time, with all the possible worlds coexisting in some sort of ‘super-space’ and ‘super-time’ coalescing in a moment. Then, the analysis shows that the story is a deterministic system by means of the moment-bound nature of the events. Thirdly, “The Garden” is sensitive to initial conditions because small changes generate infinite bifurcations. A close reading through the recursive symmetries across narrative levels confirms the structural pattern and elicits the experience of time as being complex and dynamic.

The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1) Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2) Dissatisfied with explaining a low gravitational entropy as the product of a 'special' scalar field, some theorists argue (following Boltzmann) for a 'more natural' initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background. The initial conditions of inflationary models are as natural as the equilibrium background favored by many theorists., Comment: 10 pages, 5 figures

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in LCDM models. From N-body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models., Comment: 22 pages, 8 figures, matches published version

A number of congestion control schemes which adopt the max-min fairness criterion and do not require maintenance of per flow states within the network have been proposed in the literature. The establishment of global asymptotic stability remains an open challenging research topic. In this paper, we show global asymptotic stability of two decentralized max-min congestion controllers in the absence and presence of queueing dynamics when the propagation delays are assumed to be zero. In particular, we show that these max-min congestion control schemes applied to a network of arbitrary topology, guarantee that the user sending rates converge asymptotically to the max-min allocation values for any arbitrary feasible initial condition. The second algorithm which accounts for queueing dynamics, typical in store and forward networks, does not only guarantee convergence of the sending rates to their max-min allocation values but also guarantees that the queue sizes within the network all converge to zero when there is only one bottleneck link at each path. © The authors 2015. 34 1 179 201

Accurate estimates for petrophysical properties are very important in the oil and gas industry. For two-phase flow in porous media, experimental techniques for determining these properties can be difficult to set up and can take a very long time. Generalization of these experimental results for the whole reservoir requires adapting boundary and environmental conditions which may require a large num- ber of experimental set-ups, hence emphasizing the need for numerical methods. Several numerical techniques like pore network models have been used in the past to estimate and quantify transport properties like relative permeability in reservoir rocks. These network models are however mostly restricted to quasi-static condi- tions and have many free parameters; thus are not easily predictive. An alternative is to carry out simulations directly on imaged samples of rock micro-structure using lattice Boltzmann techniques which are far more able to handle complex geometrical boundaries than classical computational fluid dynamics techniques. In this thesis, we examine the effect of four initialization techniques namely; the Euclidean Distance Transform, Covering Radius Transform, Capillary Drainage Transform, and Uniform Random distribution on the final fluid distribution in a porous media. These techniques were applied to a reconstructed sample of Fontainebleau sandstone. The convergence of the initial saturations to steady state is quantified by the Minkowski functionals and the capillary drainage transform is shown to be the most stable of the four initialization techniques. Three lattice Boltzmann (Shan-Chen, the Color Gradient, and the Free Energy) approaches are also introduced for two phase simulation in a 2D geometry. The methods are vali- dated against standard test cases in 2D. The Shan-Chen solver was then applied to a reconstructed sample of Fontainebleau sandstone for the different initial conditions. Furthermore, the initial conditions are compared with regard to discretisation ef- fects and with regard to speed of convergence. For the simple case of 2D simulations we also apply a body force to the two phase simulation. In three dimensions, we use a two relaxation time (scheme which is known for its better accuracy and stability) Shan and Chen lattice Boltzmann approach to simulate fluid redistribution for the different initial conditions studied in the thesis.

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The shape of a drop on an inclined hysteretic surface has been studied both theoretically and experimentally in this paper. Surface Evolver (SE) has been used to model the shape of the drop. The triple line was initially circular. The energy minimization method from SE is coupled with a triple line dynamics model to incorporate contact angle hysteresis (CAH) into the simulations. Experiments have also been performed with sessile drops on tilting surfaces to validate the results obtained from the SE model. From this study, two critical inclination angles are identified that describe the incipient motion of the drop. The moving angle is the first critical inclination angle at which the triple line is on the verge of being deformed from a given initial shape. The sliding angle is the second critical inclination angle at which the entire drop is in a state of impending motion. It was observed that the moving angle is a strong function of the initial contact angle. It was observed to increase initially and then decrease as the initial contact angle is increased. The sliding angle decreased monotonically as the initial contact angle is increased. A quantitative correlation is developed to explain the sliding angle as a function of the initial conditions. The predictions of this correlation have been shown to compare well with the experimental data from this study as well as with the literature. � 2014 Elsevier B.V.

In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogeneous boundary conditions of the first kind. The uniqueness and existence of a regular solution of the problem are proved. To prove the main result we use the spectral decomposition method., UPM/700-2/1/GPB/2017/9590200

The effect of antecedent conditions and specific rock fragment coverage on precipitation-driven soil erosion dynamics through multiple rainfall events was investigated using a pair of 6-m × 1-m flumes with 2.2% slope. Four sequential experiments – denoted E1, E2, E3 and E4, involved 2-h precipitation (rates of 28, 74, 74 and 28 mm h-1, respectively) and 22 h without rainfall – were conducted. In each experiment, one flume was bare while the other had 40% rock fragment coverage. The soil was hand-cultivated and smoothed before the first event (E1) only, and left untouched subsequently. Sediment yields at the flume exit reached steady-state conditions over time scales that increased with sediment size. Experiments were designed such that both steady and non-steady effluent sediment yields were reached at the conclusion of E1. Results from subsequent experiments showed that short-time soil erosion was dependent on whether steady-state erosion was achieved during the preceding event, although consistent steady-state effluent sediment yields were reached for each sediment size class. Steady-state erosion rates were, however, dependent on the rainfall intensity and its duration. If steady-state sediment yields were reached for a particular size class, that class’s effluent sediment yield peaked rapidly in the next rainfall event. The early peak was followed by a gradual decline to the steady-state condition. On the other hand, for size classes in which steady state was not reached at the end of the rainfall event (i.e., E1), in the following event (E2), the sediment yields for those classes increased gradually to steady state, i.e., the sharp peak was not observed. The effect of rock fragment cover (40%) on the soil surface was also found to be significant in terms of the time to reach steady state, i.e., their presence reduced the time for steady conditions to be attained. Effluent sediment yields for the bare and rock fragment-covered flumes (E1) showed steady conditions were reached for the latter, in contrast to the former. We used the Hairsine-Rose (H-R) model to simulate the experimental data as it explicitly models soil particle size classes. Experiments E1 and E2 involved soil compaction by raindrops, and in this case the model predictions were found to be unsatisfactory. However, compaction was effectively completed by the end of experiment E2, and the model provided reasonable predictions for experiments E3 and E4.

Experimental evidence is needed to verify the hypothesis that the memory of initial conditions is retained at late times in variable density flows. If true, this presents an opportunity to design and control late-time turbulence, with an improved understanding in the prediction of inertial confinement fusion and other general fluid mixing processes. In this communication, an experimental and theoretical study on the effects of initial condition parameters, namely, the amplitude (0) and wavenumber kappa 0 (kappa 0=2 Pi/lambda 0, where lambda(0) is the initial wavelength) of perturbations, on late-time turbulence and mixing in shock-driven Richtmyer-Meshkov (R-M) unstable fluid layers in a 2D plane is presented. Single and multi-mode membrane-free initial conditions in the form of a gas curtain having a light-heavy-light configuration (air-SF6-air) with an Atwood number of A= 0.57 were used in our experiments. A planar shock wave with a shock Mach number M= 1.21 drives the R-M instability, and the evolution of this instability after incident shock is captured using high resolution simultaneous planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) diagnostics. Time evolution of statistics such as amplitude of the mixing layer, 2D turbulent kinetic energy, Reynolds number, rms of velocity fluctuations, probability density functions, and density-specific volume correlation were observed to quantify the amount of mixing and understand the nature of turbulence in this flow. Based on these results, it was found that the R-M mixing layer is asymmetric and non-Boussinesq. There is a correlation between initial condition parameters and large-scale, and small-scale mixing at late times, indicating an initial condition dependence on R-M mixing.

We propose a nonlinear control law based on sliding mode control technique to stabilize a mobile robot while adhering to the physical constraints on its configuration variables. The notion of constrained stabilization is used to prove the stability of the closed-loop system. A key contribution is the design of controller gains in accordance to the restrictions on the initial condition domain. The proposed technique is validated through both numerical simulation and experimental results. � 1993-2012 IEEE.

Developed a calculation-experimental method of determining the initial conditions of road traffic accidents in their consequences in the event of a frontal collision.

This paper examines dynamic binary response and multi-spell duration model approaches to analyzing longitudinal discrete-time binary outcomes. Prototypical dynamic binary response models specify low-order Markovian state dependence and restrict the effects of observed and unobserved heterogeneity on the probability of transitioning into and out of a state to have the same magnitude and opposite signs. In contrast, multi-spell duration models typically allow for state-specify c duration dependence, and allow the probability of entry into and exit from a state to vary flexibly. We show that both of these approaches are special cases within a general framework. We compare specific dynamic binary response and multi-spell duration models empirically using a case study of poverty transitions. In this example, both the specification of state dependence and the restrictions on the state-specific transition probabilities imposed by the simpler dynamic binary response models are severely rejected against the more flexible multi-spell duration models. Consistent with recent literature, we conclude that the standard dynamic binary response model is unacceptably restrictive in this context.

We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus-nucleus collisions, obtained for the first time using a new analysis method based on multiparticle cumulants in mixed harmonics. This novel method is robust against systematic biases originating from nonflow effects and by construction any dependence on symmetry planes is eliminated. We demonstrate that correlations of flow harmonics exhibit a better sensitivity to medium properties than the individual flow harmonics. The new measurements are performed in Pb-Pb collisions at the center-of-mass energy per nucleon pair of root S-NN = 2.76 TeV by the ALICE experiment at the Large Hadron Collider. The centrality dependence of correlation between event-by-event fluctuations of the elliptic upsilon 2 and quadrangular upsilon 4 flow harmonics, as well as of anticorrelation between upsilon 2 and triangular upsilon 3 flow harmonics are presented. The results cover two different regimes of the initial state configurations: geometry dominated (in midcentral collisions) and fluctuation dominated (in the most central collisions). Comparisons are made to predictions from Monte Carlo Glauber, viscous hydrodynamics, AMPT, and HIJING models. Together with the existing measurements of the individual flow harmonics the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions.

We use a large sample of isolated dark matter halo pairs drawn from cosmological N-body simulations to identify candidate systems whose kinematics match that of the Local Group of Galaxies (LG). We find, in agreement with the "timing argument" and earlier work, that the separation and approach velocity of the Milky Way (MW) and Andromeda (M31) galaxies favour a total mass for the pair of $\sim 5\times 10^{12} \,M_{\odot}$. A mass this large, however, is difficult to reconcile with the small relative tangential velocity of the pair, as well as with the small deceleration from the Hubble flow observed for the most distant LG members. Halo pairs that match these three criteria have average masses a factor of $\sim 2$ times smaller than suggested by the timing argument, but with large dispersion. Guided by these results, we have selected $12$ halo pairs with total mass in the range $1.6$-$3.6 \times 10^{12}\,M_{\odot}$ for the APOSTLE project (A Project Of Simulating The Local Environment), a suite of hydrodynamical resimulations at various numerical resolution levels (reaching up to $\sim10^{4}\,M_{\odot}$ per gas particle) that use the subgrid physics developed for the EAGLE project. These simulations reproduce, by construction, the main kinematics of the MW-M31 pair, and produce satellite populations whose overall number, luminosities, and kinematics are in good agreement with observations of the MW and M31 companions. The APOSTLE candidate systems thus provide an excellent testbed to confront directly many of the predictions of the $\Lambda$CDM cosmology with observations of our local Universe., Comment: replaced with the accepted version